There is an unsupported remark in the Wikipedia article on Data indicating that visual effects artist Clay Dale had written "Ode to Spot".
However, according to this Q & A session with Brent Spiner, "Ode to Spot" was most likely written by Brannon Braga, a Star Trek producer and the writer of the episode "Schisms" in which it first appeared (and also the episode "A Fistful of Data", where the poem appeared again).
AUDIENCE MEMBER: Hi, Brent, do you still remember "Ode to Spot"?
SPINER: What, "Ode to Spot"? Um, Felus cattus is your taxonomic — wait — nomenclature, an endothermic quadruped, carniverous by nature. Go ahead (to the audience). You know what, I knew it by heart once. Um, it was a great poem actually. I think, er, I think Brannon Braga wrote that poem. Brannon's a wonderful writer really, and he's such a perverse human being and the stuff that he comes up with is always interesting. I really, really like working with Brannon. He wrote "Ode to Spot" which is, I think, Pulitzer Prize stuff. Yuh?
(Note: the heading of the web page for the Q & A session says "1977" when it should say "1997".)